Hi yes is the answer to your question it will help but it will need to be emptied quite often another thing that can cause a lot of condensation are large amounts of plants in the room
there is a saying " heat and ventilation stops condensation " so it may be that there is not enough air changes in the room and so adding to the problem
Double glazing will help but its not the be and the end all
i Know it sounds silly but try to have some air bricks put in then you will see the difference

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